RU-ALLRUSSIAN 1971 Problem 13

n is a positive integer. S is the set of all triples (a, b, c) such that $1 \leq a, b, c, \leq n$ . What is the smallest subset X of triples such that for every member of S one can find a member of X which differs in only one position. [For example, for $n = 2$ , one could take $X = \{ (1, 1, 1), (2, 2, 2) \} .$ ]